This　paper　presents　a　novel　recurrent　neural　network　for　solving　nonlinear　optimization　problems　with　inequality　constraints.　Under　the　condition　that　the　Hessian　matrix　of　the　associated　Lagrangian　function　is　positive　semidefinite,　it　is　shown　that　the　proposed　neural　network　is　stable　at　a　Karush-Kuhn-Tucker　point　in　the　sense　of　Lyapunov　and　its　output　trajectory　is　globally　convergent　to　a　minimum　solution.　Compared　with　variety　of　the　existing　projection　neural　networks,　including　their　extensions　and　modification,　for　solving　such　nonlinearly　constrained　optimization　problems,　it　is　shown　that　the　proposed　neural　network　can　solve　constrained　convex　optimization　problems　and　a　class　of　constrained　nonconvex　optimization　problems　and　there　is　no　restriction　on　the　initial　point.　Simulation　results　show　the　effectiveness　of　the　proposed　neural　network　in　solving　nonlinearly　constrained　optimization　problems.